Shonan旋转平均法：基于$SO(p)^n$的全局最优性
Shonan Rotation Averaging: Global Optimality by Surfing $SO(p)^n$
摘要：
Shonan Rotation Averaging是一种快速、简单、优雅的旋转平均算法，保证在对测量噪声的温和假设下恢复全局最优解。我们的方法采用半定松弛，以恢复证明全球最优解的旋转平均问题。与之前的工作相比，我们展示了如何使用流形最小化（仅略微）高维旋转流形来解决这些松弛的大规模实例，重新使用现有的高性能（但局部）运动结构管道。因此，我们的方法保留了当前SFM方法的速度和可扩展性，同时恢复全局最优解。
英文摘要：
Shonan Rotation Averaging is a fast, simple, and elegant rotation averaging algorithm that is guaranteed to recover globally optimal solutions under mild assumptions on the measurement noise. Our method employs semidefinite relaxation in order to recover provably globally optimal solutions of the rotation averaging problem. In contrast to prior work, we show how to solve large-scale instances of these relaxations using manifold minimization on (only slightly) higher-dimensional rotation manifolds, re-using existing high-performance (but local) structure-from-motion pipelines. Our method thus preserves the speed and scalability of current SFM methods, while recovering globally optimal solutions.
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